Given,

$\displaystyle f:\mathbb{R}^n\to \mathbb{R}$

countinous on a ball, has a critical point on $\displaystyle \bold{x}$ is there a way to determine whether or not this point is a relative extrema?

I am asking this because, there is a foolproof method for single variables called first-derivative test. But for two variables the second-partials test is not foolproof. I wish to know if there is one that is for two and more variables?